A boat initially traveling at 10 meters per second accelerates uniformly at the rate of 5.0 meters per second squared for 10 seconds. How far does the boat travel during this time?
d = Vo*t + 0.5at^2,
d = 10*10 + 0.5*5*10^2,
d = 100 + 250 = 350 m.
To find the distance traveled by the boat during this time, we can use the formula for distance traveled with uniform acceleration:
\[s = ut + \frac{1}{2}at^2\]
where:
- s is the distance traveled
- u is the initial velocity
- a is the acceleration
- t is the time
Given:
u = 10 m/s (initial velocity)
a = 5.0 m/s² (acceleration)
t = 10 s (time)
Now we can substitute the given values into the formula to find the distance:
\[s = (10 m/s)(10 s) + \frac{1}{2}(5.0 m/s²)(10 s)^2\]
First, let's calculate the first term:
\[10 m/s \times 10 s = 100 m\]
Next, let's calculate the second term:
\[\frac{1}{2} \times 5.0 m/s² \times (10 s)^2 = \frac{1}{2} \times 5.0 m/s² \times 100 s² = 250 m\]
Now we can add the two terms to find the total distance traveled:
\[s = 100 m + 250 m = 350 m\]
Therefore, the boat traveled a distance of 350 meters during this 10-second interval.
To find the distance traveled by the boat during this time, we can use the formula for calculating distance with constant acceleration:
Distance = Initial velocity * time + (1/2) * acceleration * time^2
Given:
Initial velocity (u) = 10 m/s
Acceleration (a) = 5.0 m/s^2
Time (t) = 10 s
Plugging in these values into the formula, we can calculate the distance traveled by the boat:
Distance = 10 m/s * 10 s + (1/2) * 5.0 m/s^2 * (10 s)^2
= 100 m + (1/2) * 5.0 m/s^2 * 100 s^2
= 100 m + 0.5 * 5.0 m/s^2 * 10000 s
= 100 m + 0.5 * 5.0 m/s^2 * 10000 s
= 100 m + 0.5 * 50000 m
= 100 m + 25000 m
= 25100 m
Therefore, the boat travels a distance of 25100 meters during this time.